Companions are no longer available in the store and can only be found in sales already on horses.
Companions were animals and insects which could be bought at the store. Starting at 8 months old, you could give your horse a companion. Once assigned to a horse, a companion couldn't be changed and stayed for the rest of the horse's life.
However, they have been discontinued. Horses who had companions kept them, but are now unable to play with them. The companion would wake up when you performed an action with your horse. Horses with companions are now considered valuable.